Simplify the following expression: $a = \dfrac{27x^2}{27x^2 - 117x}$ You can assume $x \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $27x^2 = (3\cdot3\cdot3 \cdot x \cdot x)$ The denominator can be factored: $27x^2 - 117x = (3\cdot3\cdot3 \cdot x \cdot x) - (3\cdot3\cdot13 \cdot x)$ The greatest common factor of all the terms is $9x$ Factoring out $9x$ gives us: $a = \dfrac{(9x)(3x)}{(9x)(3x - 13)}$ Dividing both the numerator and denominator by $9x$ gives: $a = \dfrac{3x}{3x - 13}$